Which expression is equivalent to -1/2 (3- 2/5) ?

Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.

max2010maxim [7]

Answer:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

Step-by-step explanation:

We want to write the trignometric expression:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0$

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

$\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)$

Take the secant of both sides:

$\displaystyle \sec(\theta)=\frac{u}{10}$

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

$\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}$

By substitutition:

$\displaystyle= \sin(2\theta)$

Using an double-angle identity:

$=2\sin(\theta)\cos(\theta)$

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

$\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)$

Simplify. Therefore:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

4 0

3 years ago

Give right triangle PQR, which representa the value of sin (P)?

Komok [63]

sinR = $\frac{QR}{PQ}$

noting that the sin ratio = $\frac{opposite}{hypotenuse}$

opposite to ∠P is QR and hypotenuse is PQ ( opposite right angle )

4 0

3 years ago

Read 2 more answers

9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d

kotegsom [21]

Answer:

$\frac{}{d}$ = −0.26

$s_{d}$ = 0.4219

Step-by-step explanation:

Given:

Sample1: 98.1 98.8 97.3 97.5 97.9

Sample2: 98.7 99.4 97.7 97.1 98.0

Sample 1 Sample 2 Difference d

98.1 98.7 -0.6

98.8 99.4 -0.6

97.3 97.7 -0.4

97.5 97.1 0.4

97.9 98.0 -0.1

To find:

Find the values of $\frac{}{d}$ and $s_{d}$

d overbar ( $\frac{}{d}$ ) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5

$\frac{}{d}$ = ∑d/n

= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5

= −1.3 / 5

$\frac{}{d}$ = −0.26

s Subscript d is the sample standard deviation of the difference which is calculated as following:

$s_{d}$ = √∑( $d_{i}$ - $\frac{}{d}$ )²/ n-1

$s_{d}$ =

√ $(-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1$

= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −

(−0.26))² + (−0.1 − (−0.26))² / 5−1

= $\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }$

= $\sqrt{\frac{0.712}{4} }$

= $\sqrt{0.178}$

= 0.4219

$s_{d}$ = 0.4219

Subscript d represent

μ $_{d}$ represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.

3 0

3 years ago

PLEASE HELP

rusak2 [61]

C' ( 4, -2 )

this is the explanation sort of

c ( -2, -3 ), since it is translated six units to the right, add 6 to the x-coordinate and since it is translated one unit up, add 1 to the y-coordinate

7 0

3 years ago

Read 2 more answers

Mrs.Cheng has $18 deducted monthly from checking account for her gym membership. What integer represents the change in her accou

Vikki [24]

First you would have to multiply $18 (The cost for each month) and 12 (the number of months in a year) and the answer would be 216
So she deducts 216 a year, so the answer would have to be negative

The final answer is -216

4 0

3 years ago